The government will be "stepping up to a new, active role", Mrs May said.
The plan was published in a green paper as she held her first regional cabinet meeting in the north-west of England.
Broadband, transport and energy are highlighted in a bid to "align central government infrastructure investment with local growth priorities".
The 10-point plan involves:
- Investing in science, research and innovation
- Developing skills
- Upgrading infrastructure
- Supporting business to start and grow
- Improving government procurement
- Encouraging trade and inward investment
- Delivering affordable energy and clean growth
- Cultivating world-leading sectors
- Driving growth across the whole country
- Creating the right institutions to bring together sectors and places
"This active government will build on Britain's strategic strengths and tackle our underlying weaknesses, like low productivity."
The green paper sets out ways in which the government can provide support to businesses by addressing regulatory barriers, agreeing trade deals and helping to establish institutions that encourage innovation and skills development.
Mrs May also plans to boost STEM (science, technology, engineering and maths) skills, digital skills and numeracy, including extending specialist maths schools, while £170m will be invested in creating new institutes of technology.
Business leaders welcomed the plan, which also aims to boost life sciences and low-emission vehicles.